If I am correct in the above, a private club can certainly adopt TOS and Chess.com Community Policies as their rules for the club and the admin team could enforce them if they wish. That is what I have done with many of the clubs I have been involved in.
Chess.com rules for public areas vs private clubs.

It's become evident that all of this can't be said enough. A lot of people are ignorant and dismissive of these rules even though they have been repeatedly exposed to them. It might be a good idea for people to read them again every month.

I wonder if most here adopt TOS and the chess.com Community Policies as rules for their club... or make your own club rules?

Yes an interesting subject , many subjects imo should be left out of chess completely , they have no place in chess , and that includes chess.com who are just as guilty of breaking their own rules.
I have personal views on certain subjects in life that I keep to myself , I feel quite strongly about keeping politics religion etc out of chess , but if it is forced on me then I will have an opinion.

Chess.com's terms of service for the main forums generally also apply to official clubs such as the Cheating Forum, Pro Chess League, and the official clubs for variants. This means no politics, religion, offensive, abusive, or otherwise inappropriate content, and no discussion of cheating. No public accusations - not merely of cheating but also of other negative behaviour.
Obviously, in the Cheating Forum, discussion of cheating is permitted, although the rule against public accusations still applies.
Within private clubs, admins can, to a large extent, set their own rules. You can choose to allow politics or religion. Images and other content that would not normally be permitted in the main forums can sometimes be permitted in private clubs - although if it's something potentially offensive or that should arguably be age-restricted the club should have its forums set to be visible only to members, and should probably be set so that admins have to approve new members who apply to join. If you want to allow explicit images in your private club, it would also be good to run it by the support team just to get confirmation on what specifically is and is not permitted and what conditions they want to put on permitting it (for example, they might want you to have procedures in place to keep children out).
Also, some content is never permitted. Obvious examples include illegal content; copyright violations, inappropriate images of minors, etc. Some images that might not be illegal might still be considered sufficiently extreme that they are not welcome on the site even within a private club - again, if you want to permit something like that, check with the support team first. Also, while admins can choose to permit their members to use language that would normally be considered too abusive for the main forums, sufficiently extreme cases of stalking and abuse will not be permitted; sexual harassment is not likely to be tolerated even within a private club.
Basically, admins can relax certain rules if they want, but in some cases they should check with the support team first.

If someone wants a short version of chess.com rules for public areas and the official clubs, below would be used:
Community Conduct Policy
- Be kind, helpful, and forgiving
- Do not abuse, attack, threaten, discriminate, or mistreat other members in any way
- Do not hijack threads, troll, or post distracting or meaningless content
- Do not post spam, advertisements, or copy/paste comments and messages
- Do not excessively promote your club
- Do not publicly debate religious or political topics
- Do not post obscene or pornographic content
- Do not discuss illegal activities
- Do not open more than one account
https://www.chess.com/community

Chess.com's terms of service for the main forums generally also apply to official clubs such as the Cheating Forum, Pro Chess League, and the official clubs for variants. This means no politics, religion, offensive, abusive, or otherwise inappropriate content, and no discussion of cheating. No public accusations - not merely of cheating but also of other negative behaviour.
Obviously, in the Cheating Forum, discussion of cheating is permitted, although the rule against public accusations still applies.
Within private clubs, admins can, to a large extent, set their own rules. You can choose to allow politics or religion. Images and other content that would not normally be permitted in the main forums can sometimes be permitted in private clubs - although if it's something potentially offensive or that should arguably be age-restricted the club should have its forums set to be visible only to members, and should probably be set so that admins have to approve new members who apply to join. If you want to allow explicit images in your private club, it would also be good to run it by the support team just to get confirmation on what specifically is and is not permitted and what conditions they want to put on permitting it (for example, they might want you to have procedures in place to keep children out).
Also, some content is never permitted. Obvious examples include illegal content; copyright violations, inappropriate images of minors, etc. Some images that might not be illegal might still be considered sufficiently extreme that they are not welcome on the site even within a private club - again, if you want to permit something like that, check with the support team first. Also, while admins can choose to permit their members to use language that would normally be considered too abusive for the main forums, sufficiently extreme cases of stalking and abuse will not be permitted; sexual harassment is not likely to be tolerated even within a private club.
Basically, admins can relax certain rules if they want, but in some cases they should check with the support team first.
This is a great post. I agree with all of it. I do adopt the vast majority of this in my own clubs and even in my adults clubs I’ll only allow it to go so far.

It seems clear that club owners and superadmins and moderators on admin teams
can apply TOS or their own rules or policies as they see fit.
And that they can interpret that TOS and their own rules and policies as they see fit too.
Not a bad thing.
But its also clear they can form and apply On The Spot policies - their's - at whatever time too.
And that perhaps is the most important thing. And that's a good thing too.
Not always though.

See https://www.chess.com/community:
In the Community Conduct Policy section:
"Do not post spam, advertisements, or copy/paste comments and messages"
and
"Do not excessively promote your club"
That would not be a complete blanket ban on sending messages with club links under any circumstances, but it would prohibit the spamming of such messages.
Everyone should be familiar with Chess.com Community Policies and TOS
https://www.chess.com/community
https://www.chess.com/agreement
What sometimes causes confusion is whether these apply to just the public areas at chess.com or also private clubs and private messages/private chat.
I believe TOS and the Community Policies refer to the public areas of chess.com and do not govern private clubs.
For example:
1) The "Chess.com Community Policies" has "Do not publicly debate religious or political topics" which some private clubs allow (think of some of the discussion clubs).
2) TOS has "post any comments, text, messages, or links in the forums or any public comments that contain any advertisements of any kind, including religious, political, or recruiting messages for Chess.com groups, clubs, blogs, or any other content on or off of Chess.com" while some clubs allow for club recruiting messages and club and/or match advertisements.
3) The Community Policies has "Be kind, helpful, and forgiving" and TOS has no "harassing, defamatory" post. In my experience from reporting, chess.com staff sets a much higher bar for such posts in private clubs versus public areas.
4) TOS has "invasive of another's privacy". In my experience, any quote or screenshot from a private message or private chat that identifies the sender and put him in a negative light would be deleted by staff in the public areas but rarely in private clubs.
5) TOS prohibits "vulgar, obscene, sexually explicit" but some private clubs allow some of such content. Think of Playboy Warrior which I believe allows for partial (or whole?) nudity which is not allowed for pubic avatars or in public forums.
https://www.chess.com/club/playboy-chess-warriors
6) TOS prohibits "objectionable" posts. The private clubs are free (within certain limits) to set their own rules for what is allowed or not.
7) TOS prohibits "post any comments, text, messages, or links in the forums or any public comments that is off topic or irrelevant to the purpose and content of the original content, game, article, blog, or forum topic;". Private clubs are free to make their own rules and some of the Free Speech discussion clubs have no rules against spam.
In conclusion, the TOS refers several times to "the [public] forums or any public comments". My understanding is the TOS and "Chess.com Community Policies" govern all the public areas of chess.com.
That said, there is a smaller set of site-wide rules which govern all content on chess.com including private clubs and private messages and chat. These include a prohibition of sexual harassment, extreme personal harassment, clear racism (including the use of the N-word and other racial slurs).